{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:LRXQ2JRE6F7UXOJUUHJZ75VGLS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0bb8d08ada06fbc86951c7a0caceafafc7a91daaf43acf43f5816b7536b33f51","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-01T00:26:59Z","title_canon_sha256":"0d51da95b90250a6a6b6cd7734ada3691310791713c7490417d584bd889be529"},"schema_version":"1.0","source":{"id":"2206.00161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.00161","created_at":"2026-07-05T05:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"2206.00161v2","created_at":"2026-07-05T05:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.00161","created_at":"2026-07-05T05:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"LRXQ2JRE6F7U","created_at":"2026-07-05T05:40:46Z"},{"alias_kind":"pith_short_16","alias_value":"LRXQ2JRE6F7UXOJU","created_at":"2026-07-05T05:40:46Z"},{"alias_kind":"pith_short_8","alias_value":"LRXQ2JRE","created_at":"2026-07-05T05:40:46Z"}],"graph_snapshots":[{"event_id":"sha256:b749aecb5836be5d174c84e5d48f70c94017d4d52dd48fa4f4c4b207831aa516","target":"graph","created_at":"2026-07-05T05:40:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.00161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we solve the asymptotic Plateau problem in hyperbolic space for constant $\\sigma_{n-1}$ curvature, i.e. the existence of a complete hypersurface in $\\mathbb{H}^{n+1}$ satisfying $\\sigma_{n-1}(\\kappa)=\\sigma\\in (0,n)$ with a prescribed asymptotic boundary $\\Gamma$. The key ingredient is the curvature estimates. Previously, this is only known for $\\sigma_0<\\sigma<n$, where $\\sigma_0$ is a positive constant.","authors_text":"Siyuan Lu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-01T00:26:59Z","title":"On the asymptotic Plateau problem in hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.00161","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a36090558fe241ee151462c4ff5bc6df9e1392f70f3bd8cb8fcfa8c3e2c12e3b","target":"record","created_at":"2026-07-05T05:40:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0bb8d08ada06fbc86951c7a0caceafafc7a91daaf43acf43f5816b7536b33f51","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-01T00:26:59Z","title_canon_sha256":"0d51da95b90250a6a6b6cd7734ada3691310791713c7490417d584bd889be529"},"schema_version":"1.0","source":{"id":"2206.00161","kind":"arxiv","version":2}},"canonical_sha256":"5c6f0d2624f17f4bb934a1d39ff6a65c900700dfb28b1848e23c9ffb5bfc1422","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c6f0d2624f17f4bb934a1d39ff6a65c900700dfb28b1848e23c9ffb5bfc1422","first_computed_at":"2026-07-05T05:40:46.321993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:40:46.321993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YoGLGlYK3aGP7gYPT0KGTVOT0v2xsdduzmWOH+zMxbDnb8qXwsV2TU9G4HKkeUi84GfL0u6WpbWQPqqqxl42Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:40:46.322492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.00161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a36090558fe241ee151462c4ff5bc6df9e1392f70f3bd8cb8fcfa8c3e2c12e3b","sha256:b749aecb5836be5d174c84e5d48f70c94017d4d52dd48fa4f4c4b207831aa516"],"state_sha256":"c5b9cc81a96e148f6e4f859fa78f07b35e01387f50bd6b4554de39fb187ee6a1"}